Pricing Strategy & Industrial Organization
Klemperer Switching-Cost Bargain-Then-Ripoff Formula
Calculate Paul Klemperer’s (1987, 1995) below-cost Period-1 customer acquisition price P_1* = c_1 + t - delta*s, Period-2 lock-in harvest price P_2* = c_2 + s, and lifecycle customer profit.
Why inkjet printers, espresso machines, and cloud migrations sell below cost in Period 1!
Paul Klemperer (1987, 1995) and Joseph Farrell & Paul Klemperer (2007) explained the ubiquitous "Bargain-Then-Ripoff" pricing pattern across enterprise software, printers/ink, razors/blades, and banking! Suppose competing Hotelling vendors (horizontal differentiation t > 0, Period-1 hardware/onboarding cost c_1) acquire customers in Period 1 who then face Switching Cost s >= 0 when buying Period-2 consumables/renewals (unit cost c_2, firm discount factor delta in [0, 1]). In Period 2, each vendor extracts lock-in markup s via Ripoff Renewal Price P_2* = c_2 + s! Anticipating discounted Period-2 harvest profit delta * s per Period-1 buyer, vendors bid away that entire lock-in rent upfront in Period 1, slashing Period-1 Bargain Price to P_1* = c_1 + t - delta * s (dropping strictly BELOW unit manufacturing cost c_1 whenever delta * s > t!)!
Verify on Period1_Hardware_Cost c_1 = 100.00 (B2), Brand_Differentiation t = 25.00 (B3), Period2_Consumable_Cost c_2 = 10.00 (B4), Switching_Cost s = 40.00 (B5), and Discount_Factor delta = 0.90 (B6): Without lock-in (s = 0), Period-1 Price would be 100 + 25 = 125.00; WITH s = 40 lock-in, Period-1 Acquisition Price drops to 100 + 25 - (0.90 * 40) = 89.00 (-$11.00 loss-leader subsidy below $100 cost!), Period-2 Renewal Price jumps to 10 + 40 = 50.00 (+$40.00 harvest margin), and Discounted Two-Period Lifecycle Profit per Buyer equals (89 - 100) + 0.90 * (50 - 10) = -11.00 + 36.00 = 25.00 (= exact differentiation rent t = 25.00!)!
| Switching-Cost Pricing Metric (c_1=100, t=25, c_2=10, s=40, delta=0.90) | Formula | Verified Output |
|---|---|---|
| Period-1 Bargain Acquisition Price (P_1*) | c_1 + t - delta * s | 89.00 (-$11 Below Cost!) |
| Period-1 Upfront Margin (P_1* - c_1) | t - delta * s | -11.00 (CAC Loss Leader) |
| Period-2 Locked-In Harvest Price (P_2*) | c_2 + s | 50.00 (+$40 Lock-In Margin) |
| Discounted Lifecycle Profit per Buyer | (P_1* - c_1) + delta*(P_2* - c_2) | 25.00 (Rent Competed Away!) |
Klemperer Period-1 Bargain Acquisition Price P_1* Formula
Validate non-negative unit costs c_1, c_2 >= 0, differentiation t > 0, switching cost s >= 0, and discount factor 0 <= delta <= 1.
=LET(c_1, B2, t_df, B3, s_sw, B5, dl_f, B6, IF(OR(c_1 < 0, t_df <= 0, s_sw < 0, dl_f < 0, dl_f > 1), "Invalid Switching-Cost Input", ROUND(c_1 + t_df - dl_f * s_sw, 2)))Discounted Two-Period Lifecycle Profit per Customer Formula
Notice Farrell-Klemperer rent dissipation: raising switching cost s from 40 to 60 lowers P_1* further to 71.00 while raising P_2* to 70.00, leaving lifecycle equilibrium profit unchanged at 25.00!
=LET(c_1, B2, t_df, B3, c_2, B4, s_sw, B5, dl_f, B6, IF(OR(c_1 < 0, t_df <= 0, c_2 < 0, s_sw < 0, dl_f < 0, dl_f > 1), "Invalid Switching-Cost Input", LET(p_1, c_1 + t_df - dl_f * s_sw, p_2, c_2 + s_sw, ROUND((p_1 - c_1) + dl_f * (p_2 - c_2), 2))))Try the example
Use the original values or change them to test your understanding.